Question

question 1
1 pts
two sides of a triangle measure 5 and 7 inches. between what two measures can the third side be?
between and

question 2
1 pts
two sides of a triangle measure 10 and 25 inches. between what two measures can the third side be?
between and

Explanation:

Question 1

Step1: Recall triangle inequality theorem

The triangle inequality theorem states that the length of the third side of a triangle must be greater than the absolute difference of the other two sides and less than the sum of the other two sides. For sides \(a\) and \(b\), the third side \(c\) satisfies \(|a - b| < c < a + b\).
Here, \(a = 5\) and \(b = 7\). First, calculate the difference: \(|5 - 7| = | - 2| = 2\). Then, calculate the sum: \(5 + 7 = 12\).

Step2: Determine the range for the third side

So, the third side must be greater than \(2\) and less than \(12\).

Step1: Apply triangle inequality theorem

Using the triangle inequality theorem \(|a - b| < c < a + b\), where \(a = 10\) and \(b = 25\). Calculate the difference: \(|10 - 25| = | - 15| = 15\). Calculate the sum: \(10 + 25 = 35\).

Step2: Find the range for the third side

Thus, the third side must be greater than \(15\) and less than \(35\).

Answer:

Between \(2\) and \(12\)

Question 2